Overlap, Regularity, and Flowering Phenologies

Stiles (1977) presented the results of a study of the flowering phenologies of 11 tropical plants that are pollinated by hummingbirds. He concluded that the peaks of flowering times were uniformly spaced and interpreted this spacing as the result of competition for pollinating hummingbirds. Competition for pollinators would result in selection for staggered flowering times, and thus a uniform spacing of flowering peaks, to improve the efficiency of intraspecific pollination and minimize interspecific hybridization. Poole and Rathcke (1979) dispute the observation of Stiles that the flowering peaks are uniformly spaced. They present the results of a statistical test of Stile's data on flowering phenologies. The statistic that they use compares the intervals between dates of peak flowering with the intervals between randomly spaced points. Their sample statistic P is the variance of distances between the flowering peaks of temporally adjacent species. The expected variance, E(P), under their null hypothesis that flowering dates are randomly assigned, is the expected variance of the broken-stick distribution. For k species, then, k P/E(P) is distributed approximately as a x2 with k degrees of freedom and allows a test of the null hypothesis P = E(P). Values of the ratio P/E(P) near one indicate that the observed variance equals the expected variance and that the flowering peaks are distributed randomly within the growing season. Values of this ratio less than or greater than one indicate uniform or clumped dispersion patterns, respectively, for the peaks of flowering. Poole and Rathcke obtained P/E(P) ratios of 2.07, 1.85, 2.05, and 2.03 for the 4 yr of data, and concluded that far from being uniformly spaced, the peaks of flowering were clumped. This result is not surprising in view of the fact that they calculated these ratios on the assumption of a uniform growing season. As Stiles (1979) points out, there is a peak of flowering in the dry season and one in the wet season. Both of these seasons have a characteristic and nonoverlapping set of flowering species. In order to properly apply the test that Poole and Rathcke suggest, one must break the year into a dry and a wet season. If one follows the same conventions that Poole and Rathcke adopt in their article, but distinguishes the dry season flora and the wet season flora, the conclusion is totally different. Table 1 shows the values for P/E(P) and the degrees of freedom for each growing season and each year. All but one of the values of P/E(P) is less than one. This suggests that the peaks of flowering are more regularly spaced than one would expect from a random model (a total x2 value of 15.31 with 35 df is significant at the 1% level). Regardless of the results of the previous analysis, one may dispute the use of the variance of the broken-stick distribution as a null hypothesis on two grounds. Of